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Certifying the Thurston norm via SL\((2,\mathbb{C})\)-twisted homology. (English) Zbl 1452.57011

Thurston, Dylan P. (ed.), What’s next? The mathematical legacy of William P. Thurston. Princeton, NJ: Princeton University Press. Ann. Math. Stud. 205, 1-20 (2020).
For a large class of hyperbolic knots including fibered knots, the conjecture from [N. M. Dunfield et al., Exp. Math. 21, No. 4, 329–352 (2012; Zbl 1266.57008)] is proved that the hyperbolic torsion polynomial (a refined version of the twisted Alexander polynomial) determines the Seifert genus of the knot.
For the entire collection see [Zbl 1437.55002].

MSC:

57K14 Knot polynomials
57K30 General topology of 3-manifolds

Biographic References:

Thurston, Bill
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